Error analysis of the moment method
Error analysis of the moment method
复制标题
矩量法误差分析
DOI：
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复制
发表时间：
2004
影响因子：
3.5
通讯作者：
Weng Cho Chew
中科院分区：
文献类型：
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作者：
K. Warnick;Weng Cho Chew
由于矩量法在辐射和散射问题模拟中的广泛应用，求解误差的分析和控制成为计算电磁学中一个重要的问题。要解决的物理问题、其网格表示和数值方法都影响精度。尽管基准测试等经验方法在实践中几乎完全用于代码验证和准确性评估，但近年来已经获得了许多重要的理论结果，包括收敛证明和解决方案误差估计。这项工作回顾了基本概念，如误差测量的类型，问题的性质和影响误差的数值方法，最优性原理和基本近似误差估计。分析了几种散射体的表面电流和散射幅度误差，包括边角奇点和正交误差的影响。我们还回顾了由于共振效应和迭代线性系统解的收敛速率而引起的病态的结果。
Because of the widespread use of the Method of Moments for simulation of radiation and scattering problems, analysis and control of solution error is a significant concern in computational electromagnetics. The physical problem to be solved, its mesh representation, and the numerical method all impact accuracy. Although empirical approaches such as benchmarking are used almost exclusively in practice for code validation and accuracy assessment, a number of significant theoretical results have been obtained in recent years, including proofs of convergence and solution-error estimates. This work reviews fundamental concepts such as types of error measures, properties of the problem and numerical method that affect error, the optimality principle, and basic approximation error estimates. Analyses are given for surface-current and scattering-amplitude errors for several scatterers, including the effects of edge and corner singularities and quadrature error. We also review results on ill-conditioning due to resonance effects and the convergence rates of iterative linear-system solutions.